### Re: 1, 2, 3 and to the 4: Getting Back into the Numbers Game

Posted:

**Thu Apr 16, 2020 2:12 pm**One math class that I've constantly used throughout life was algebra. If moving on to advanced classes is the goal, then it will be well worth the effort to go through it, covering all the topics.

quadratic functions, logs and exponents, graphs, system of equations, matrices, inequalities, radical functions,.. etc. I mean every bit of it is very useful.

The rules for the topics covered in algebra will be used over and over again in later advanced classes.

In geometry, I would be sure to understand the anatomy of a circle and the triangle. What's a chord? what's a secant? What makes 45-45-90 and 30-60-90 special? What's a sector? It will also teach you to be able to do simple proofs in a logical manner.

Then I would spend a lot of time learning trigonometry. The anatomy of a periodic function, graphing a periodic function, the ratios in a triangle, the unit circle, the identities, angle formulas and proofs, and the theorems such as de moivre, euler equation.. etc.

The algebra and trig will serve as the foundation for calculus. Now calculus will be different. You will need to start thinking. Definitions will become important. Concepts will become important - i.e. first thing you'll hit, what's a limit? What's continuity? Then you'll really learn what a slope is and that there are different kinds of slopes. They are useful! Things tucked away in alg, trig and geometry will be put to use to form a new concept in the very first chapter of calculus and it goes on from there. Many many ideas in calculus.

All of calculus (usually broken in 3 parts) is useful. Calculus will be what alg, trig and geometry was for later classes.

Then there is diff eq. I strongly suggest DiPrima for that one, it is a great book. Then Linear algebra. These go hand in hand.

Things get really interesting when you get to partial differential equations. This is when you start to realize that the many abstract ideas learned in the past can now be applied to approximate and solve real life problems. The wave equation, the heat equation, just as a small sample to solve things like a drum beat, a heating point source, etc.

And some of these solutions are borrowed to solve problems in finance - black scholes for example and the heat equation.

While these later classes are exciting (for some) the one truly useful class was algebra. It will be used over and over again. Algebra is like the rules for moving the chess pieces and applies to all of the strategies ever concocted.

quadratic functions, logs and exponents, graphs, system of equations, matrices, inequalities, radical functions,.. etc. I mean every bit of it is very useful.

The rules for the topics covered in algebra will be used over and over again in later advanced classes.

In geometry, I would be sure to understand the anatomy of a circle and the triangle. What's a chord? what's a secant? What makes 45-45-90 and 30-60-90 special? What's a sector? It will also teach you to be able to do simple proofs in a logical manner.

Then I would spend a lot of time learning trigonometry. The anatomy of a periodic function, graphing a periodic function, the ratios in a triangle, the unit circle, the identities, angle formulas and proofs, and the theorems such as de moivre, euler equation.. etc.

The algebra and trig will serve as the foundation for calculus. Now calculus will be different. You will need to start thinking. Definitions will become important. Concepts will become important - i.e. first thing you'll hit, what's a limit? What's continuity? Then you'll really learn what a slope is and that there are different kinds of slopes. They are useful! Things tucked away in alg, trig and geometry will be put to use to form a new concept in the very first chapter of calculus and it goes on from there. Many many ideas in calculus.

All of calculus (usually broken in 3 parts) is useful. Calculus will be what alg, trig and geometry was for later classes.

Then there is diff eq. I strongly suggest DiPrima for that one, it is a great book. Then Linear algebra. These go hand in hand.

Things get really interesting when you get to partial differential equations. This is when you start to realize that the many abstract ideas learned in the past can now be applied to approximate and solve real life problems. The wave equation, the heat equation, just as a small sample to solve things like a drum beat, a heating point source, etc.

And some of these solutions are borrowed to solve problems in finance - black scholes for example and the heat equation.

While these later classes are exciting (for some) the one truly useful class was algebra. It will be used over and over again. Algebra is like the rules for moving the chess pieces and applies to all of the strategies ever concocted.